Harmonies

%load_ext autoreload
%autoreload 2
import os
from collections import Counter
from statistics import mean

import dimcat as dc
import ms3
import pandas as pd
from dimcat import plotting
from dimcat.utils import grams, make_transition_matrix
import utils

pd.set_option("display.max_rows", 1000)
pd.set_option("display.max_columns", 500)

RESULTS_PATH = os.path.abspath(os.path.join(utils.OUTPUT_FOLDER, "harmonies"))
os.makedirs(RESULTS_PATH, exist_ok=True)


def make_output_path(
    filename: str,
    extension=None,
    path=RESULTS_PATH,
) -> str:
    return utils.make_output_path(filename=filename, extension=extension, path=path)


def save_figure_as(
    fig, filename, formats=("png", "pdf"), directory=RESULTS_PATH, **kwargs
):
    if formats is not None:
        for fmt in formats:
            plotting.write_image(fig, filename, directory, format=fmt, **kwargs)
    else:
        plotting.write_image(fig, filename, directory, **kwargs)

Loading data

D = utils.get_dataset("couperin_concerts", corpus_release="v2.2")
D

Dataset
=======
{'inputs': {'basepath': None,
            'packages': {'couperin_concerts': ["'couperin_concerts.measures' (MuseScoreMeasures)",
                                               "'couperin_concerts.notes' (MuseScoreNotes)",
                                               "'couperin_concerts.expanded' (MuseScoreHarmonies)",
                                               "'couperin_concerts.chords' (MuseScoreChords)",
                                               "'couperin_concerts.metadata' (Metadata)"]}},
 'outputs': {'basepath': None, 'packages': {}},
 'pipeline': []}

All labels

labels = D.get_feature("harmonylabels")
labels

			mc	mn	quarterbeats	duration_qb	mc_onset	mn_onset	timesig	staff	voice	volta	label	pedal	numeral	form	figbass	changes	relativeroot	cadence	phraseend	chord_type	chord_tones	added_tones	root	bass_note	alt_label	globalkey_is_minor	localkey_is_minor	globalkey_mode	localkey_mode	localkey_resolved	localkey_and_mode	root_roman	relativeroot_resolved	effective_localkey	effective_localkey_resolved	effective_localkey_is_minor	pedal_resolved	chord_and_mode	chord_reduced	chord_reduced_and_mode	applied_to_numeral	numeral_or_applied_to_numeral	intervals_over_bass	intervals_over_root	scale_degrees	scale_degrees_and_mode	scale_degrees_major	scale_degrees_minor	globalkey	localkey	chord
corpus	piece	i
couperin_concerts	c01n01_prelude	0	1	0	0	2.00	0	1/2	4/4	1	1	<NA>	G.I{	<NA>	I	<NA>	<NA>	<NA>	<NA>	<NA>	{	M	(0, 4, 1)	()	0	0	<NA>	False	False	major	major	I	I, major	I	NaN	I	I	False	<NA>	I, major	I	I, major	<NA>	I	(M3, P5)	(M3, P5)	(1, 3, 5)	(1, 3, 5), major	(1, 3, 5)	(1, #3, 5)	G	I	I
		1	2	1	2	2.00	0	0	4/4	1	1	<NA>	V	<NA>	V	<NA>	<NA>	<NA>	<NA>	<NA>	<NA>	M	(1, 5, 2)	()	1	1	<NA>	False	False	major	major	I	I, major	V	NaN	I	I	False	<NA>	V, major	V	V, major	<NA>	V	(M3, P5)	(M3, P5)	(5, 7, 2)	(5, 7, 2), major	(5, 7, 2)	(5, #7, 2)	G	I	V
		2	2	1	4	0.50	1/2	1/2	4/4	1	1	<NA>	I6	<NA>	I	<NA>	6	<NA>	<NA>	<NA>	<NA>	M	(4, 1, 0)	()	0	4	<NA>	False	False	major	major	I	I, major	I	NaN	I	I	False	<NA>	I6, major	I6	I6, major	<NA>	I	(m3, m6)	(M3, P5)	(3, 5, 1)	(3, 5, 1), major	(3, 5, 1)	(#3, 5, 1)	G	I	I6
		3	2	1	9/2	0.50	5/8	5/8	4/4	1	1	<NA>	I	<NA>	I	<NA>	<NA>	<NA>	<NA>	<NA>	<NA>	M	(0, 4, 1)	()	0	0	<NA>	False	False	major	major	I	I, major	I	NaN	I	I	False	<NA>	I, major	I	I, major	<NA>	I	(M3, P5)	(M3, P5)	(1, 3, 5)	(1, 3, 5), major	(1, 3, 5)	(1, #3, 5)	G	I	I
		4	2	1	5	0.75	3/4	3/4	4/4	1	1	<NA>	V(4)	<NA>	V	<NA>	<NA>	4	<NA>	<NA>	<NA>	M	(1, 0, 2)	()	1	1	<NA>	False	False	major	major	I	I, major	V	NaN	I	I	False	<NA>	V(4), major	V	V, major	<NA>	V	(P4, P5)	(P4, P5)	(5, 1, 2)	(5, 1, 2), major	(5, 1, 2)	(5, 1, 2)	G	I	V(4)
	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
	parnasse_07	230	52	52	411/2	0.25	3/8	3/8	4/4	1	1	<NA>	i64	<NA>	i	<NA>	64	<NA>	<NA>	<NA>	<NA>	m	(1, 0, -3)	()	0	1	<NA>	True	True	minor	minor	i	i, minor	i	NaN	i	i	True	<NA>	i64, minor	i64	i64, minor	<NA>	i	(P4, m6)	(m3, P5)	(5, 1, 3)	(5, 1, 3), minor	(5, 1, b3)	(5, 1, 3)	b	i	i64
		231	52	52	823/4	0.25	7/16	7/16	4/4	1	1	<NA>	iio64	<NA>	ii	o	64	<NA>	<NA>	<NA>	<NA>	o	(-4, 2, -1)	()	2	-4	<NA>	True	True	minor	minor	i	i, minor	ii	NaN	i	i	True	<NA>	iio64, minor	iio64	iio64, minor	<NA>	ii	(a4, M6)	(m3, d5)	(6, 2, 4)	(6, 2, 4), minor	(b6, 2, 4)	(6, 2, 4)	b	i	iio64
		232	52	52	206	1.00	1/2	1/2	4/4	1	1	<NA>	i6	<NA>	i	<NA>	6	<NA>	<NA>	<NA>	<NA>	m	(-3, 1, 0)	()	0	-3	<NA>	True	True	minor	minor	i	i, minor	i	NaN	i	i	True	<NA>	i6, minor	i6	i6, minor	<NA>	i	(M3, M6)	(m3, P5)	(3, 5, 1)	(3, 5, 1), minor	(b3, 5, 1)	(3, 5, 1)	b	i	i6
		233	52	52	207	1.00	3/4	3/4	4/4	1	1	<NA>	V	<NA>	V	<NA>	<NA>	<NA>	<NA>	<NA>	<NA>	M	(1, 5, 2)	()	1	1	<NA>	True	True	minor	minor	i	i, minor	V	NaN	i	i	True	<NA>	V, minor	V	V, minor	<NA>	V	(M3, P5)	(M3, P5)	(5, #7, 2)	(5, #7, 2), minor	(5, 7, 2)	(5, #7, 2)	b	i	V
		234	53	53	208	4.00	0	0	4/4	1	1	<NA>	i|PAC}	<NA>	i	<NA>	<NA>	<NA>	<NA>	PAC	}	m	(0, -3, 1)	()	0	0	<NA>	True	True	minor	minor	i	i, minor	i	NaN	i	i	True	<NA>	i, minor	i	i, minor	<NA>	i	(m3, P5)	(m3, P5)	(1, 3, 5)	(1, 3, 5), minor	(1, b3, 5)	(1, 3, 5)	b	i	i

8376 rows × 51 columns

metadata = D.get_metadata()
is_annotated_mask = metadata.label_count > 0
is_annotated_index = dc.PieceIndex(metadata.index[is_annotated_mask])
annotated_notes = D.get_feature("notes").subselect(is_annotated_index)
print(f"The annotated pieces have {len(annotated_notes)} notes.")

The annotated pieces have 35542 notes.

Delete @none labels This creates progressions between the label before and after the @none label that might not actually be perceived as transitions!

df = utils.remove_none_labels(labels.df)

Length before: 8376
There are 0 @none labels which we are going to delete.
Length after: 8376

Delete non-chord labels (typically, phrase labels)

df = utils.remove_non_chord_labels(df)

Length before: 8376
There are 0 non-chord labels which we are going to delete:

Series([], Name: count, dtype: Int64)

Length after: 8376

key_region_groups, key_region2key = ms3.adjacency_groups(df.localkey)
df["key_regions"] = key_region_groups

Unigrams

k = 25
df.chord.value_counts().iloc[:k]

chord
V        1175
I         965
i         763
V65       470
I6        420
V7        413
i6        395
V43       303
ii%65     233
IV        212
V2        177
ii65      176
V6        154
V(4)      130
ii%43     128
vi        123
iv        112
ii        108
IV6       102
iv6        69
i64        69
V(64)      69
ii7        65
ii6        58
VI         57
Name: count, dtype: Int64

font_dict = {"font": {"size": 20}}
H_LAYOUT = utils.STD_LAYOUT.copy()
H_LAYOUT.update(
    {
        "legend": dict(
            {"orientation": "h", "itemsizing": "constant", "x": -0.05}, **font_dict
        )
    }
)

fig = utils.plot_cum(
    df.chord,
    x_log=True,
    markersize=4,
    left_range=(-0.03, 3.7),
    right_range=(-0.01, 1.11),
    **H_LAYOUT,
)
save_figure_as(fig, "chord_label_unigram_distribution")
fig

Unigrams in major segments

minor, major = df[df.localkey_is_minor], df[~df.localkey_is_minor]
print(
    f"{len(major)} tokens ({len(major.chord.unique())} types) in major and {len(minor)} "
    f"({len(minor.chord.unique())} types) in minor."
)

4138 tokens (119 types) in major and 4238 (169 types) in minor.

major.chord.value_counts().iloc[:k]

chord
I        906
V        615
I6       416
V65      232
V7       228
IV       165
ii65     159
V43      131
vi       122
V6       117
ii        89
IV6       83
V(4)      81
V2        79
ii7       52
ii6       41
V(64)     40
I64       34
vi7       33
V43/V     32
ii43      30
V65/V     28
vi6       28
iii6      24
IVM7      22
Name: count, dtype: Int64

fig = utils.plot_cum(
    major.chord,
    x_log=True,
    markersize=4,
    left_range=(-0.03, 3.7),
    right_range=(-0.01, 1.11),
    **H_LAYOUT,
)
save_figure_as(fig, "chord_label_unigram_distribution_in_major")
fig.show()

Unigrams in minor segments

print(
    f"{len(major)} tokens ({len(major.chord.unique())} types) in major and {len(minor)} "
    f"({len(minor.chord.unique())} types) in minor."
)

4138 tokens (119 types) in major and 4238 (169 types) in minor.

minor.chord.value_counts().iloc[:k]

chord
i         761
V         560
i6        394
V65       238
ii%65     230
V7        185
V43       172
ii%43     128
iv        112
V2         98
iv6        69
i64        69
I          59
VI         57
V(4)       49
VIM7       47
IV         47
V65/iv     45
v6         43
V6         37
ii%7       34
iio        33
III        32
V(64)      29
iv7        26
Name: count, dtype: Int64

fig = utils.plot_cum(
    minor.chord,
    x_log=True,
    markersize=4,
    left_range=(-0.03, 3.7),
    right_range=(-0.01, 1.11),
    **H_LAYOUT,
)
save_figure_as(fig, "chord_label_unigram_distribution_in_minor")
fig.show()

Bigrams

chord_successions = [s.to_list() for _, s in df.groupby("key_regions").chord]

gs = grams(chord_successions)
c = Counter(gs)

dict(sorted(c.items(), key=lambda a: a[1], reverse=True)[:k])

{('V', 'I'): 256,
 ('V7', 'I'): 206,
 ('V', 'i'): 196,
 ('I', 'V'): 167,
 ('i', 'V'): 154,
 ('V65', 'I'): 153,
 ('V', 'V7'): 144,
 ('V7', 'i'): 124,
 ('ii%65', 'V'): 123,
 ('V65', 'i'): 123,
 ('V', 'I6'): 119,
 ('V65', 'V7'): 111,
 ('V(4)', 'V'): 101,
 ('ii65', 'V'): 89,
 ('I6', 'I'): 86,
 ('V43', 'i'): 85,
 ('V43', 'I'): 84,
 ('V2', 'i6'): 83,
 ('i6', 'V43'): 82,
 ('V', 'i6'): 81,
 ('I', 'I6'): 74,
 ('V2', 'I6'): 67,
 ('I6', 'ii65'): 64,
 ('V', 'V2'): 64,
 ('i6', 'ii%65'): 63}

Absolute Counts (read from index to column)

make_transition_matrix(chord_successions, k=k, distinct_only=True)

	I	i	V	V7	I6	i6	V43	ii65	V2	ii%65	V65	IV	V6	ii	vi	V(4)	ii%43	iv	v6	VI	IV6	ii7	IVM7	IV64	iii6
V	256	196	0	144	119	81	11	0	64	2	56	0	24	11	5	0	9	1	5	1	16	0	0	1	14
V7	206	124	2	0	2	5	1	0	1	0	9	0	0	0	14	0	0	0	0	8	2	0	0	0	0
I	0	3	167	30	74	0	22	37	8	0	46	49	46	1	40	32	0	0	0	0	11	4	14	14	1
i	1	0	154	3	0	55	25	3	9	40	59	15	14	0	0	13	21	11	24	17	2	1	0	0	0
V65	153	123	15	111	2	9	6	0	3	0	0	0	1	0	1	0	1	0	0	0	0	0	0	0	0
ii%65	0	9	123	4	0	16	1	0	7	0	2	0	0	0	0	20	6	0	0	0	0	2	0	0	0
V(4)	0	0	101	20	0	0	0	0	0	0	1	0	2	0	0	0	0	0	0	0	0	0	0	0	1
ii65	6	1	89	6	3	0	0	0	8	0	0	0	1	3	0	20	0	0	0	0	2	8	0	0	1
I6	86	0	32	1	0	0	62	64	1	0	10	35	10	1	13	15	0	0	0	0	4	15	2	0	0
V43	84	85	4	3	25	45	0	0	2	0	32	0	2	0	0	0	0	0	0	0	0	0	0	1	0
V2	2	3	1	0	67	83	7	0	0	0	2	0	1	0	0	0	0	0	0	0	0	0	0	0	1
i6	0	55	23	1	0	0	82	4	2	63	41	4	3	0	0	7	4	7	0	9	0	0	0	0	0
IV6	4	0	2	5	5	0	1	1	0	0	55	6	3	3	0	0	0	0	0	0	0	2	0	0	2
V(64)	1	0	54	8	0	0	0	0	0	1	0	1	0	0	0	2	0	0	0	0	0	0	0	0	0
ii%43	0	0	43	9	0	5	3	0	0	45	1	0	0	0	0	0	0	0	0	0	0	1	0	0	0
IV	11	0	10	0	25	0	24	3	4	0	8	0	1	41	1	2	0	1	0	0	6	14	1	0	0
ii	0	0	38	13	0	1	0	0	1	0	12	4	7	0	5	0	0	0	0	0	3	2	0	0	0
vi	3	0	1	0	21	0	1	31	1	2	8	17	0	0	0	0	0	0	0	0	9	0	2	0	1
VIM7	0	0	2	0	0	0	0	0	0	0	0	0	0	0	0	0	31	0	0	0	0	0	0	0	0
V43/V	0	0	31	0	0	0	0	0	0	0	0	0	0	0	0	3	0	0	0	0	0	1	0	0	0
ii7	1	0	29	10	6	0	4	0	0	0	5	0	0	0	0	0	0	0	0	0	0	0	0	0	0
V65/iv	0	0	0	0	0	0	0	0	0	0	0	3	0	0	0	0	0	29	0	0	0	0	0	0	0
V6	23	10	26	4	9	3	0	0	1	0	8	0	0	0	9	0	0	0	6	0	1	0	0	0	1
VI	0	0	0	0	0	2	0	6	0	21	0	0	0	0	0	0	0	5	0	0	0	0	0	0	0
i64	0	2	0	1	0	5	4	0	17	5	1	0	0	0	0	0	20	0	0	0	0	0	0	0	0

Normalized Counts

make_transition_matrix(
    chord_successions, k=k, distinct_only=True, normalize=True, decimals=2
)

	I	i	V	V7	I6	i6	V43	ii65	V2	ii%65	V65	IV	V6	ii	vi	V(4)	ii%43	iv	v6	VI	IV6	ii7	IVM7	IV64	iii6
V	0.23	0.17	0.00	0.13	0.11	0.07	0.01	0.00	0.06	0.00	0.05	0.00	0.02	0.01	0.00	0.00	0.01	0.00	0.00	0.00	0.01	0.00	0.00	0.00	0.01
V7	0.50	0.30	0.00	0.00	0.00	0.01	0.00	0.00	0.00	0.00	0.02	0.00	0.00	0.00	0.03	0.00	0.00	0.00	0.00	0.02	0.00	0.00	0.00	0.00	0.00
I	0.00	0.00	0.24	0.04	0.10	0.00	0.03	0.05	0.01	0.00	0.07	0.07	0.07	0.00	0.06	0.05	0.00	0.00	0.00	0.00	0.02	0.01	0.02	0.02	0.00
i	0.00	0.00	0.25	0.00	0.00	0.09	0.04	0.00	0.01	0.07	0.10	0.02	0.02	0.00	0.00	0.02	0.03	0.02	0.04	0.03	0.00	0.00	0.00	0.00	0.00
V65	0.33	0.26	0.03	0.24	0.00	0.02	0.01	0.00	0.01	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
ii%65	0.00	0.04	0.53	0.02	0.00	0.07	0.00	0.00	0.03	0.00	0.01	0.00	0.00	0.00	0.00	0.09	0.03	0.00	0.00	0.00	0.00	0.01	0.00	0.00	0.00
V(4)	0.00	0.00	0.79	0.16	0.00	0.00	0.00	0.00	0.00	0.00	0.01	0.00	0.02	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.01
ii65	0.03	0.01	0.51	0.03	0.02	0.00	0.00	0.00	0.05	0.00	0.00	0.00	0.01	0.02	0.00	0.11	0.00	0.00	0.00	0.00	0.01	0.05	0.00	0.00	0.01
I6	0.21	0.00	0.08	0.00	0.00	0.00	0.15	0.15	0.00	0.00	0.02	0.08	0.02	0.00	0.03	0.04	0.00	0.00	0.00	0.00	0.01	0.04	0.00	0.00	0.00
V43	0.28	0.28	0.01	0.01	0.08	0.15	0.00	0.00	0.01	0.00	0.11	0.00	0.01	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
V2	0.01	0.02	0.01	0.00	0.38	0.47	0.04	0.00	0.00	0.00	0.01	0.00	0.01	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.01
i6	0.00	0.14	0.06	0.00	0.00	0.00	0.21	0.01	0.01	0.16	0.10	0.01	0.01	0.00	0.00	0.02	0.01	0.02	0.00	0.02	0.00	0.00	0.00	0.00	0.00
IV6	0.04	0.00	0.02	0.05	0.05	0.00	0.01	0.01	0.00	0.00	0.54	0.06	0.03	0.03	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.02	0.00	0.00	0.02
V(64)	0.01	0.00	0.78	0.12	0.00	0.00	0.00	0.00	0.00	0.01	0.00	0.01	0.00	0.00	0.00	0.03	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
ii%43	0.00	0.00	0.34	0.07	0.00	0.04	0.02	0.00	0.00	0.35	0.01	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.01	0.00	0.00	0.00
IV	0.06	0.00	0.05	0.00	0.13	0.00	0.12	0.02	0.02	0.00	0.04	0.00	0.01	0.21	0.01	0.01	0.00	0.01	0.00	0.00	0.03	0.07	0.01	0.00	0.00
ii	0.00	0.00	0.36	0.12	0.00	0.01	0.00	0.00	0.01	0.00	0.11	0.04	0.07	0.00	0.05	0.00	0.00	0.00	0.00	0.00	0.03	0.02	0.00	0.00	0.00
vi	0.03	0.00	0.01	0.00	0.19	0.00	0.01	0.28	0.01	0.02	0.07	0.15	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.00	0.02	0.00	0.01
VIM7	0.00	0.00	0.04	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.65	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
V43/V	0.00	0.00	0.89	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.09	0.00	0.00	0.00	0.00	0.00	0.03	0.00	0.00	0.00
ii7	0.02	0.00	0.45	0.15	0.09	0.00	0.06	0.00	0.00	0.00	0.08	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
V65/iv	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.07	0.00	0.00	0.00	0.00	0.00	0.64	0.00	0.00	0.00	0.00	0.00	0.00	0.00
V6	0.16	0.07	0.18	0.03	0.06	0.02	0.00	0.00	0.01	0.00	0.05	0.00	0.00	0.00	0.06	0.00	0.00	0.00	0.04	0.00	0.01	0.00	0.00	0.00	0.01
VI	0.00	0.00	0.00	0.00	0.00	0.04	0.00	0.13	0.00	0.46	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.11	0.00	0.00	0.00	0.00	0.00	0.00	0.00
i64	0.00	0.03	0.00	0.01	0.00	0.07	0.06	0.00	0.25	0.07	0.01	0.00	0.00	0.00	0.00	0.00	0.29	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00

Entropy

make_transition_matrix(
    chord_successions, k=k, IC=True, distinct_only=True, smooth=1, decimals=2
)

	I	i	V	V7	I6	i6	V43	ii65	V2	ii%65	V65	IV	V6	ii	vi	V(4)	ii%43	iv	v6	VI	IV6	ii7	IVM7	IV64	iii6
V	2.40	2.79	10.41	3.23	3.50	4.05	6.83	10.41	4.39	8.83	4.58	10.41	5.77	6.83	7.83	10.41	7.09	9.41	7.83	9.41	6.32	10.41	10.41	9.41	6.50
V7	1.64	2.37	7.75	9.34	7.75	6.75	8.34	9.34	8.34	9.34	6.02	9.34	9.34	9.34	5.43	9.34	9.34	9.34	9.34	6.17	7.75	9.34	9.34	9.34	9.34
I	9.88	7.88	2.49	4.93	3.65	9.88	5.36	4.63	6.71	9.88	4.33	4.24	4.33	8.88	4.52	4.84	9.88	9.88	9.88	9.88	6.30	7.56	5.97	5.97	8.88
i	8.72	9.72	2.44	7.72	9.72	3.91	5.02	7.72	6.40	4.36	3.81	5.72	5.81	9.72	9.72	5.91	5.26	6.14	5.08	5.55	8.14	8.72	9.72	9.72	9.72
V65	2.19	2.51	5.46	2.65	7.87	6.14	6.65	9.46	7.46	9.46	9.46	9.46	8.46	9.46	8.46	9.46	8.46	9.46	9.46	9.46	9.46	9.46	9.46	9.46	9.46
ii%65	8.88	5.55	1.92	6.55	8.88	4.79	7.88	8.88	5.88	8.88	7.29	8.88	8.88	8.88	8.88	4.48	6.07	8.88	8.88	8.88	8.88	7.29	8.88	8.88	8.88
V(4)	8.51	8.51	1.84	4.12	8.51	8.51	8.51	8.51	8.51	8.51	7.51	8.51	6.93	8.51	8.51	8.51	8.51	8.51	8.51	8.51	8.51	8.51	8.51	8.51	7.51
ii65	5.88	7.69	2.19	5.88	6.69	8.69	8.69	8.69	5.52	8.69	8.69	8.69	7.69	6.69	8.69	4.29	8.69	8.69	8.69	8.69	7.10	5.52	8.69	8.69	7.69
I6	2.90	9.34	4.30	8.34	9.34	9.34	3.37	3.32	8.34	9.34	5.88	4.17	5.88	8.34	5.54	5.34	9.34	9.34	9.34	9.34	7.02	5.34	7.76	9.34	9.34
V43	2.67	2.65	6.75	7.08	4.38	3.55	9.08	9.08	7.49	9.08	4.03	9.08	7.49	9.08	9.08	9.08	9.08	9.08	9.08	9.08	9.08	9.08	9.08	8.08	9.08
V2	7.11	6.69	7.69	8.69	2.60	2.30	5.69	8.69	8.69	8.69	7.11	8.69	7.69	8.69	8.69	8.69	8.69	8.69	8.69	8.69	8.69	8.69	8.69	8.69	7.69
i6	9.29	3.49	4.71	8.29	9.29	9.29	2.92	6.97	7.71	3.29	3.90	6.97	7.29	9.29	9.29	6.29	6.97	6.29	9.29	5.97	9.29	9.29	9.29	9.29	9.29
IV6	6.08	8.41	6.82	5.82	5.82	8.41	7.41	7.41	8.41	8.41	2.60	5.60	6.41	6.41	8.41	8.41	8.41	8.41	8.41	8.41	8.41	6.82	8.41	8.41	6.82
V(64)	7.26	8.26	2.48	5.09	8.26	8.26	8.26	8.26	8.26	7.26	8.26	7.26	8.26	8.26	8.26	6.67	8.26	8.26	8.26	8.26	8.26	8.26	8.26	8.26	8.26
ii%43	8.51	8.51	3.05	5.19	8.51	5.93	6.51	8.51	8.51	2.99	7.51	8.51	8.51	8.51	8.51	8.51	8.51	8.51	8.51	8.51	8.51	7.51	8.51	8.51	8.51
IV	5.17	8.75	5.29	8.75	4.05	8.75	4.11	6.75	6.43	8.75	5.58	8.75	7.75	3.36	7.75	7.17	8.75	7.75	8.75	8.75	5.94	4.84	7.75	8.75	8.75
ii	8.42	8.42	3.13	4.61	8.42	7.42	8.42	8.42	7.42	8.42	4.72	6.10	5.42	8.42	5.83	8.42	8.42	8.42	8.42	8.42	6.42	6.83	8.42	8.42	8.42
vi	6.45	8.45	7.45	8.45	3.99	8.45	7.45	3.45	7.45	6.86	5.28	4.28	8.45	8.45	8.45	8.45	8.45	8.45	8.45	8.45	5.13	8.45	6.86	8.45	7.45
VIM7	8.15	8.15	6.57	8.15	8.15	8.15	8.15	8.15	8.15	8.15	8.15	8.15	8.15	8.15	8.15	8.15	3.15	8.15	8.15	8.15	8.15	8.15	8.15	8.15	8.15
V43/V	8.09	8.09	3.09	8.09	8.09	8.09	8.09	8.09	8.09	8.09	8.09	8.09	8.09	8.09	8.09	6.09	8.09	8.09	8.09	8.09	8.09	7.09	8.09	8.09	8.09
ii7	7.24	8.24	3.33	4.78	5.43	8.24	5.92	8.24	8.24	8.24	5.65	8.24	8.24	8.24	8.24	8.24	8.24	8.24	8.24	8.24	8.24	8.24	8.24	8.24	8.24
V65/iv	8.14	8.14	8.14	8.14	8.14	8.14	8.14	8.14	8.14	8.14	8.14	6.14	8.14	8.14	8.14	8.14	8.14	3.23	8.14	8.14	8.14	8.14	8.14	8.14	8.14
V6	4.00	5.12	3.83	6.26	5.26	6.58	8.58	8.58	7.58	8.58	5.41	8.58	8.58	8.58	5.26	8.58	8.58	8.58	5.77	8.58	7.58	8.58	8.58	8.58	7.58
VI	8.14	8.14	8.14	8.14	8.14	6.56	8.14	5.34	8.14	3.69	8.14	8.14	8.14	8.14	8.14	8.14	8.14	5.56	8.14	8.14	8.14	8.14	8.14	8.14	8.14
i64	8.26	6.67	8.26	7.26	8.26	5.67	5.94	8.26	4.09	5.67	7.26	8.26	8.26	8.26	8.26	8.26	3.87	8.26	8.26	8.26	8.26	8.26	8.26	8.26	8.26

Minor vs. Major

region_is_minor = (
    df.groupby("key_regions")
    .localkey_is_minor.unique()
    .map(lambda values: values[0])
    .to_dict()
)
region_key = (
    df.groupby("key_regions").localkey.unique().map(lambda values: values[0]).to_dict()
)

key_chords = {
    ix: s.to_list()
    for ix, s in df.reset_index().groupby(["piece", "key_regions"]).chord
}
major, minor = [], []
for chords, is_minor in zip(key_chords.values(), region_is_minor.values()):
    (major, minor)[is_minor].append(chords)

make_transition_matrix(major, k=k, distinct_only=True, normalize=True)

	I	i	V	V7	I6	V43	i6	ii65	V65	ii%65	V6	V2	vi	IV	V(4)	ii	iv	ii%43	v6	IV6	VI	ii43	V(64)	iii6	ii2
V	0.218220	0.177966	0.000000	0.135593	0.118644	0.010593	0.067797	0.000000	0.044492	0.000000	0.021186	0.046610	0.006356	0.000000	0.000000	0.008475	0.000000	0.008475	0.004237	0.021186	0.000000	0.002119	0.000000	0.012712	0.00000
V7	0.448864	0.318182	0.005682	0.000000	0.005682	0.000000	0.017045	0.000000	0.022727	0.000000	0.000000	0.005682	0.045455	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.005682	0.034091	0.000000	0.022727	0.000000	0.00000
i	0.000000	0.000000	0.302326	0.000000	0.000000	0.062016	0.096899	0.003876	0.100775	0.054264	0.015504	0.015504	0.000000	0.023256	0.007752	0.000000	0.019380	0.034884	0.042636	0.000000	0.034884	0.000000	0.000000	0.000000	0.00000
V65	0.339806	0.252427	0.033981	0.233010	0.004854	0.024272	0.029126	0.000000	0.000000	0.000000	0.000000	0.000000	0.004854	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.00000
I	0.000000	0.003378	0.236486	0.040541	0.118243	0.040541	0.000000	0.057432	0.064189	0.000000	0.074324	0.003378	0.067568	0.060811	0.050676	0.000000	0.000000	0.000000	0.000000	0.020270	0.000000	0.003378	0.000000	0.000000	0.02027
ii%65	0.000000	0.030612	0.622449	0.010204	0.000000	0.010204	0.020408	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.091837	0.000000	0.000000	0.030612	0.000000	0.000000	0.000000	0.000000	0.071429	0.000000	0.00000
V43	0.281046	0.241830	0.019608	0.000000	0.091503	0.000000	0.137255	0.000000	0.117647	0.000000	0.013072	0.006536	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.00000
V(4)	0.000000	0.000000	0.796296	0.185185	0.000000	0.000000	0.000000	0.000000	0.018519	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.00000
ii65	0.012048	0.012048	0.445783	0.048193	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.048193	0.000000	0.000000	0.144578	0.036145	0.000000	0.000000	0.000000	0.024096	0.000000	0.096386	0.060241	0.000000	0.00000
I6	0.190476	0.000000	0.074074	0.005291	0.000000	0.179894	0.000000	0.164021	0.026455	0.000000	0.010582	0.005291	0.037037	0.084656	0.031746	0.005291	0.000000	0.000000	0.000000	0.015873	0.000000	0.005291	0.015873	0.000000	0.00000
i6	0.000000	0.143750	0.043750	0.000000	0.000000	0.206250	0.000000	0.012500	0.118750	0.162500	0.006250	0.006250	0.000000	0.006250	0.018750	0.000000	0.025000	0.012500	0.000000	0.000000	0.025000	0.000000	0.006250	0.000000	0.00000
V2	0.013889	0.013889	0.013889	0.000000	0.402778	0.069444	0.416667	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.00000
IV6	0.055556	0.000000	0.000000	0.055556	0.037037	0.018519	0.000000	0.000000	0.537037	0.000000	0.055556	0.000000	0.000000	0.018519	0.000000	0.055556	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.037037	0.018519	0.00000
V(64)	0.000000	0.000000	0.777778	0.074074	0.000000	0.000000	0.000000	0.000000	0.000000	0.037037	0.000000	0.000000	0.000000	0.000000	0.037037	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.00000
ii%43	0.000000	0.000000	0.358491	0.075472	0.000000	0.056604	0.037736	0.000000	0.018868	0.377358	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.018868	0.000000	0.00000
vi	0.017857	0.000000	0.000000	0.000000	0.250000	0.017857	0.000000	0.303571	0.071429	0.017857	0.000000	0.000000	0.000000	0.071429	0.000000	0.000000	0.000000	0.000000	0.000000	0.107143	0.000000	0.000000	0.000000	0.017857	0.00000
ii	0.000000	0.000000	0.404762	0.071429	0.000000	0.000000	0.023810	0.000000	0.095238	0.000000	0.047619	0.023810	0.047619	0.023810	0.000000	0.000000	0.000000	0.000000	0.000000	0.047619	0.000000	0.000000	0.000000	0.000000	0.00000
ii7	0.000000	0.000000	0.520000	0.120000	0.040000	0.040000	0.000000	0.000000	0.120000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.040000	0.000000	0.00000
IV	0.025000	0.000000	0.012500	0.000000	0.162500	0.137500	0.000000	0.025000	0.037500	0.000000	0.000000	0.025000	0.000000	0.000000	0.012500	0.162500	0.012500	0.000000	0.000000	0.050000	0.000000	0.012500	0.000000	0.000000	0.00000
VI	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.038462	0.076923	0.000000	0.461538	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.192308	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.00000
V6	0.203390	0.101695	0.135593	0.033898	0.016949	0.000000	0.016949	0.000000	0.050847	0.000000	0.000000	0.016949	0.084746	0.000000	0.000000	0.000000	0.000000	0.000000	0.033898	0.016949	0.000000	0.016949	0.000000	0.000000	0.00000
V65/iv	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.150000	0.000000	0.000000	0.550000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.00000
VIM7	0.000000	0.000000	0.050000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.550000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.00000
V43/V	0.000000	0.000000	0.909091	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.090909	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.00000
V7/IV	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.833333	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.00000

make_transition_matrix(minor, k=k, distinct_only=True, normalize=True)

	I	i	V	V7	I6	V43	i6	V2	V65	ii%65	ii65	IV	ii	V6	vi	iv	V(4)	ii%43	v6	IVM7	i64	IV64	V(64)	III	VI
V	0.229779	0.161765	0.000000	0.123162	0.108456	0.011029	0.082721	0.077206	0.062500	0.001838	0.000000	0.000000	0.011029	0.022059	0.001838	0.000000	0.000000	0.009191	0.005515	0.000000	0.009191	0.001838	0.000000	0.000000	0.001838
V7	0.592593	0.280423	0.005291	0.000000	0.005291	0.005291	0.010582	0.000000	0.026455	0.000000	0.000000	0.000000	0.000000	0.000000	0.021164	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.005291
I	0.000000	0.002882	0.233429	0.037464	0.103746	0.025937	0.000000	0.011527	0.074928	0.000000	0.040346	0.077810	0.002882	0.069164	0.054755	0.000000	0.040346	0.000000	0.000000	0.025937	0.000000	0.025937	0.023055	0.000000	0.000000
V65	0.311688	0.277056	0.030303	0.264069	0.004329	0.004329	0.012987	0.012987	0.000000	0.000000	0.000000	0.000000	0.000000	0.004329	0.000000	0.000000	0.000000	0.004329	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
i	0.003509	0.000000	0.217544	0.003509	0.000000	0.028070	0.091228	0.007018	0.112281	0.080702	0.007018	0.024561	0.000000	0.028070	0.000000	0.014035	0.035088	0.042105	0.042105	0.000000	0.010526	0.000000	0.010526	0.007018	0.028070
ii%65	0.000000	0.051724	0.448276	0.017241	0.000000	0.000000	0.112069	0.034483	0.017241	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.094828	0.025862	0.000000	0.000000	0.043103	0.000000	0.051724	0.000000	0.000000
V(4)	0.000000	0.000000	0.838710	0.145161	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
I6	0.227723	0.000000	0.084158	0.000000	0.000000	0.138614	0.000000	0.000000	0.024752	0.000000	0.148515	0.094059	0.000000	0.039604	0.024752	0.000000	0.024752	0.000000	0.000000	0.004950	0.000000	0.000000	0.024752	0.000000	0.000000
i6	0.000000	0.153061	0.056122	0.005102	0.000000	0.229592	0.000000	0.005102	0.107143	0.163265	0.010204	0.010204	0.000000	0.010204	0.000000	0.015306	0.020408	0.010204	0.000000	0.000000	0.000000	0.000000	0.020408	0.000000	0.020408
ii65	0.051282	0.000000	0.538462	0.025641	0.038462	0.000000	0.000000	0.038462	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.102564	0.000000	0.000000	0.000000	0.000000	0.000000	0.064103	0.000000	0.000000
V43	0.276119	0.298507	0.007463	0.014925	0.074627	0.000000	0.179104	0.007463	0.097015	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.022388	0.000000	0.000000	0.000000	0.000000
V2	0.011765	0.023529	0.000000	0.000000	0.388235	0.023529	0.458824	0.000000	0.023529	0.000000	0.000000	0.000000	0.000000	0.011765	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
V(64)	0.025641	0.000000	0.769231	0.153846	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.025641	0.000000	0.000000	0.000000	0.000000	0.025641	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
IV	0.061856	0.000000	0.051546	0.000000	0.113402	0.113402	0.000000	0.010309	0.051546	0.000000	0.010309	0.000000	0.278351	0.010309	0.010309	0.000000	0.010309	0.000000	0.000000	0.000000	0.000000	0.000000	0.010309	0.000000	0.000000
ii%43	0.000000	0.000000	0.328125	0.031250	0.000000	0.000000	0.046875	0.000000	0.000000	0.375000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.140625	0.000000	0.015625	0.000000	0.000000
IV6	0.023810	0.000000	0.023810	0.023810	0.071429	0.000000	0.000000	0.000000	0.547619	0.000000	0.023810	0.119048	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
ii	0.000000	0.000000	0.372549	0.078431	0.000000	0.000000	0.000000	0.000000	0.137255	0.000000	0.000000	0.039216	0.000000	0.098039	0.058824	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.019608	0.000000	0.000000
V43/V	0.000000	0.000000	0.863636	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.090909	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
V6	0.125000	0.050000	0.200000	0.025000	0.100000	0.000000	0.025000	0.000000	0.062500	0.000000	0.000000	0.000000	0.000000	0.000000	0.050000	0.000000	0.000000	0.000000	0.050000	0.000000	0.025000	0.000000	0.000000	0.000000	0.000000
V65/iv	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.761905	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
ii7	0.030303	0.000000	0.454545	0.151515	0.121212	0.030303	0.000000	0.000000	0.060606	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.060606	0.000000	0.000000
VIM7	0.000000	0.000000	0.047619	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.666667	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
vi	0.040816	0.000000	0.020408	0.000000	0.142857	0.000000	0.000000	0.000000	0.081633	0.020408	0.265306	0.224490	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
ii6	0.000000	0.000000	0.413793	0.000000	0.103448	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.103448	0.000000	0.000000	0.000000	0.034483	0.034483	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
i64	0.000000	0.000000	0.000000	0.031250	0.000000	0.062500	0.156250	0.250000	0.000000	0.062500	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.312500	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000

Chord progressions without suspensions

Here called plain chords, which consist only of numeral, inversion figures, and relative keys.

df["plain_chords"] = (
    df.numeral + df.figbass.fillna("") + ("/" + df.relativeroot).fillna("")
)

df.plain_chords.iloc[:k]

corpus             piece           i 
couperin_concerts  c01n01_prelude  0          I
                                   1          V
                                   2         I6
                                   3          I
                                   4          V
                                   5          V
                                   6          I
                                   7         vi
                                   8         I6
                                   9         V6
                                   10    vi43/V
                                   11     ii7/V
                                   12     V43/V
                                   13         V
                                   14        ii
                                   15     #vii7
                                   16      III7
                                   17        i6
                                   18      ii65
                                   19       V64
                                   20        V7
                                   21         I
                                   22         V
                                   23       I64
                                   24        V2
Name: plain_chords, dtype: string

Consecutive identical labels are merged

def remove_subsequent_identical(col):
    return col[col != col.shift()].to_list()


key_regions_plain_chords = (
    df.reset_index()
    .groupby(["piece", "key_regions"])
    .plain_chords.apply(remove_subsequent_identical)
)
key_plain_chords = {ix: s for ix, s in key_regions_plain_chords.items()}
major_plain, minor_plain = [], []
for chords, is_minor in zip(key_plain_chords.values(), region_is_minor.values()):
    (major_plain, minor_plain)[is_minor].append(chords)

plain_chords_per_segment = {k: len(v) for k, v in key_plain_chords.items()}

print(
    f"The local key segments have {sum(plain_chords_per_segment.values())} 'plain chords' without immediate "
    f"repetitions, yielding {len(grams(list(key_plain_chords.values())))} bigrams.\n{sum(map(len, major_plain))} "
    f"chords are in major, {sum(map(len, minor_plain))} in minor."
)

The local key segments have 7521 'plain chords' without immediate repetitions, yielding 6956 bigrams.
3217 chords are in major, 3573 in minor.

{
    segment: chord_count
    for segment, chord_count in list(
        {
            (
                piece,
                region_key[key] + (" minor" if region_is_minor[key] else " major"),
            ): v
            for (piece, key), v in plain_chords_per_segment.items()
        }.items()
    )[:k]
}

{('c01n01_prelude', 'I major'): 42,
 ('c01n01_prelude', 'ii minor'): 7,
 ('c01n01_prelude', 'V major'): 6,
 ('c01n01_prelude', 'IV major'): 5,
 ('c01n02_allemande', 'I major'): 20,
 ('c01n02_allemande', 'V major'): 21,
 ('c01n02_allemande', 'vi minor'): 10,
 ('c01n03_sarabande', 'i minor'): 15,
 ('c01n03_sarabande', 'III major'): 3,
 ('c01n03_sarabande', 'VII major'): 2,
 ('c01n03_sarabande', 'v minor'): 14,
 ('c01n04_gavotte', 'i minor'): 20,
 ('c01n04_gavotte', 'III major'): 7,
 ('c01n05_gigue', 'I major'): 46,
 ('c01n05_gigue', 'V major'): 2,
 ('c01n05_gigue', 'vi minor'): 15,
 ('c01n05_gigue', 'IV major'): 2,
 ('c01n05_gigue', 'ii minor'): 5,
 ('c01n06_menuet_en_trio', 'i minor'): 14,
 ('c01n06_menuet_en_trio', 'III major'): 8,
 ('c02n01_prelude', 'I major'): 17,
 ('c02n01_prelude', 'V major'): 4,
 ('c02n02_allemande_fuguee', 'I major'): 28,
 ('c02n02_allemande_fuguee', 'V major'): 5,
 ('c02n02_allemande_fuguee', 'IV major'): 13}

print(
    f"Segments being in the same local key have a mean length of {round(mean(plain_chords_per_segment.values()), 2)} "
    f"plain chords."
)

Segments being in the same local key have a mean length of 13.29 plain chords.

Most frequent 3-, 4-, and 5-grams in major

utils.sorted_gram_counts(major_plain, 3)

N = 548

	count	%
progression
(V, V7, I)	41	7.48
(ii65, V, V7)	32	5.84
(I, V, I)	29	5.29
(i, V, i)	29	5.29
(ii65, V, i)	27	4.93
(ii65, V, I)	27	4.93
(I6, V43, I)	26	4.74
(i6, ii65, V)	26	4.74
(V65, i, V)	25	4.56
(V, V7, i)	25	4.56
(ii43, ii65, V)	22	4.01
(V65, V7, i)	22	4.01
(V65, I, V)	21	3.83
(i6, V43, i)	20	3.65
(I6, ii65, V)	18	3.28
(IV6, V65, I)	18	3.28
(V, i, V)	18	3.28
(V, I6, I)	17	3.10
(V43, I, V)	17	3.10
(i, V65, i)	17	3.10
(I6, I, V)	15	2.74
(vi, ii65, V)	15	2.74
(i, V, V7)	15	2.74
(V43, i, V)	14	2.55
(I, V65, I)	12	2.19

utils.sorted_gram_counts(major_plain, 4)

N = 207

	count	%
progression
(ii65, V, V7, I)	16	7.73
(ii65, V, V7, i)	15	7.25
(V, I6, I, V)	11	5.31
(i6, ii65, V, i)	11	5.31
(i, V65, i, V)	9	4.35
(IV, I6, V43, I)	9	4.35
(I, V, V7, I)	9	4.35
(I6, ii65, V, I)	9	4.35
(V, I6, V43, I)	8	3.86
(vi, ii65, V, I)	8	3.86
(V65, i, V, i)	8	3.86
(V, i, V65, i)	8	3.86
(i, V, V7, i)	8	3.86
(IV, V43, I, V)	7	3.38
(V43, i, V65, i)	7	3.38
(V43, I, V, I)	7	3.38
(V43, i, V, i)	7	3.38
(IV6, V65, I, V)	7	3.38
(i6, ii65, V, V7)	7	3.38
(I6, I, V, I)	6	2.90
(V2, i6, ii65, V)	6	2.90
(V43, i6, ii65, V)	6	2.90
(i, V65, V7, i)	6	2.90
(i6, V65, i, V)	6	2.90
(V65, i, V, V7)	6	2.90

utils.sorted_gram_counts(major_plain, 5)

N = 106

	count	%
progression
(i6, ii65, V, V7, i)	6	5.66
(V, I6, I, V, I)	5	4.72
(i, V, i, V65, i)	5	4.72
(I6, I, V, V7, I)	5	4.72
(vi, ii65, V, V7, I)	5	4.72
(ii65, V, i6, V43, i)	5	4.72
(i6, V43, i, V, i)	5	4.72
(I6, ii65, V, V7, I)	4	3.77
(I6, IV, V43, I, V)	4	3.77
(V2, i6, ii65, V, i)	4	3.77
(V43, i, V65, i, V)	4	3.77
(I, IV, I6, V43, I)	4	3.77
(V65, V7, I, V65, V7)	4	3.77
(V7, I, V65, V7, I)	4	3.77
(V65, i, V, i, V65)	4	3.77
(V, i, V65, i, V)	4	3.77
(V, I6, I, V, V7)	4	3.77
(VI, ii65, V, V7, i)	4	3.77
(V65, V7, i, ii65, V)	4	3.77
(i, V, i, V, i)	4	3.77
(V, i6, V43, i, V)	4	3.77
(V65, i, i6, ii65, V)	4	3.77
(i6, V43, i, V65, V7)	4	3.77
(I, V, I6, V43, I)	3	2.83
(I, IV7, ii65, V2, I6)	3	2.83

Most frequent 3-, 4-, and 5-grams in minor

utils.sorted_gram_counts(minor_plain, 3)

N = 602

	count	%
progression
(V, V7, I)	57	9.47
(I, V, I)	44	7.31
(ii65, V, V7)	37	6.15
(i, V, i)	34	5.65
(ii65, V, I)	30	4.98
(i6, V43, i)	30	4.98
(V65, V7, I)	29	4.82
(V65, i, V)	28	4.65
(V65, I, V)	26	4.32
(V, V7, i)	24	3.99
(ii43, ii65, V)	23	3.82
(ii65, V, i)	23	3.82
(V65, V7, i)	20	3.32
(I6, V43, I)	20	3.32
(i6, ii65, V)	19	3.16
(I6, ii65, V)	17	2.82
(i, V65, i)	17	2.82
(V, I6, I)	16	2.66
(V, I, V)	16	2.66
(V43, I, V)	16	2.66
(I6, I, V)	16	2.66
(I, V, V7)	15	2.49
(V, i6, V43)	15	2.49
(i, ii65, V)	15	2.49
(V, V2, i6)	15	2.49

utils.sorted_gram_counts(minor_plain, 4)

N = 237

	count	%
progression
(ii65, V, V7, I)	23	9.70
(I, V, V7, I)	14	5.91
(ii65, V, V7, i)	13	5.49
(V65, I, V, I)	13	5.49
(vi, ii65, V, I)	11	4.64
(V65, i, V, i)	11	4.64
(V, i6, V43, i)	10	4.22
(V2, i6, V43, i)	10	4.22
(V43, i, V, i)	9	3.80
(i, ii65, V, i)	9	3.80
(i6, V43, i, V)	9	3.80
(i, V65, i, V)	9	3.80
(I6, V43, I, V)	9	3.80
(V, i, V65, i)	8	3.38
(ii65, i6, ii65, i6)	8	3.38
(I6, V, V7, I)	8	3.38
(I, V65, I, V)	7	2.95
(V65, V7, i, V)	7	2.95
(I, V65, V7, I)	7	2.95
(i6, V43, i, V65)	7	2.95
(i6, ii65, V, i)	7	2.95
(I6, ii65, V, I)	7	2.95
(I6, I, V, I)	7	2.95
(I6, ii65, V, V7)	7	2.95
(ii43, ii65, V, V7)	7	2.95

utils.sorted_gram_counts(minor_plain, 5)

N = 121

	count	%
progression
(i6, V43, i, V, i)	8	6.61
(I6, ii65, V, V7, I)	7	5.79
(V, I, V, V7, I)	6	4.96
(ii65, i6, ii65, i6, ii65)	6	4.96
(i6, ii65, i6, ii65, i6)	6	4.96
(V65, V7, I, V65, V7)	5	4.13
(V7, I, V65, V7, I)	5	4.13
(I, V65, V7, I, V65)	5	4.13
(I, ii65, V, V7, I)	5	4.13
(V, i6, V43, i, V)	5	4.13
(i, V, i, V65, i)	5	4.13
(V, i, V65, i, V)	5	4.13
(I, V7, I, V7, I)	5	4.13
(i6, ii65, V, V7, i)	4	3.31
(I, IV64, I, V, I)	4	3.31
(ii65, V, i6, V43, i)	4	3.31
(V, V2, i6, V43, i)	4	3.31
(V65, V7, i, ii65, V)	4	3.31
(I, V, V65, I, V)	4	3.31
(I, V, I, V43/V, V)	4	3.31
(IV, ii, V6, V, I6)	4	3.31
(IV, I6, V43, I, V)	4	3.31
(i6, V43, i6, ii65, V)	4	3.31
(i, V65, i, V, i)	4	3.31
(ii43, ii65, V, V7, I)	4	3.31

Counting particular progressions

MEMORY = {}
chord_progressions = list(key_plain_chords.values())


def look_for(n_gram):
    n = len(n_gram)
    if n in MEMORY:
        n_grams = MEMORY[n]
    else:
        n_grams = grams(chord_progressions, n)
        MEMORY[n] = n_grams
    matches = n_grams.count(n_gram)
    total = len(n_grams)
    return f"{matches} ({round(100*matches/total, 3)} %)"

look_for(("i", "v6"))

'17 (0.244 %)'

look_for(("i", "v6", "iv6"))

'5 (0.078 %)'

look_for(("i", "v6", "iv6", "V"))

'3 (0.051 %)'

look_for(("i", "V6", "v6"))

'1 (0.016 %)'

look_for(("V", "IV6", "V65"))

'15 (0.235 %)'

Chord progressions preceding phrase endings

def phraseending_progressions(df, n=3, k=k):
    selector = (
        df.groupby(level=0, group_keys=False)
        .phraseend.apply(lambda col: col.notna().shift().fillna(True))
        .cumsum()
    )
    print(f"{selector.max()} phrases overall.")
    phraseends = (
        df.groupby(selector)
        .apply(lambda df: df.chord.iloc[-n:].reset_index(drop=True))
        .unstack()
    )
    return (
        phraseends.groupby(phraseends.columns.to_list())
        .size()
        .sort_values(ascending=False)
        .iloc[:k]
    )

phraseending_progressions(df)

1145 phrases overall.

0      1      2
V      V7     I    75
V(4)   V      I    51
V      V7     i    42
V(64)  V      I    29
I      V      I    28
ii65   V      I    25
V(4)   V      i    24
ii%65  V      i    22
V65    i      V    20
i      V      i    20
V(64)  V      i    17
V65    I      V    14
V43    I      V    12
V(4)   V7     I    12
V7     i      V    10
ii%43  ii%65  V     9
i(4)   i      V     9
VIM7   ii%43  V     9
V      i      V     9
V65    V7     I     9
V43    i      V     8
ii%65  V      I     8
vi     ii65   V     6
V(4)   V7     i     6
I(4)   I      V     6
dtype: int64

phraseending_progressions(df, 4)

1145 phrases overall.

0      1      2   3
ii65   V      V7  I    23
ii%65  V      V7  i    20
I      V      V7  I    15
ii65   V(4)   V   I    15
I      V(4)   V   I    15
vi     ii65   V   I    14
i      V      V7  i    11
ii%65  V(4)   V   i    11
V43    I      V   I    10
I6     V      V7  I     9
V43    i      V   i     9
i      V(4)   V   i     8
I6     V(4)   V   I     8
ii%65  V(64)  V   i     8
i      ii%65  V   i     7
I      ii65   V   I     7
ii%65  V      V7  I     6
I6     V(64)  V   I     6
V65    i(4)   i   V     6
I      V(64)  V   I     6
V65    V7     i   V     6
ii65   V(64)  V   I     6
IV     V43    I   V     6
ii65   V      V7  i     5
I      V(4)   V7  I     5
dtype: int64